"""Functions for generating model components and simulated power spectra."""
import numpy as np
from fooof.core.utils import check_iter, check_flat
from fooof.core.funcs import get_ap_func, get_pe_func, infer_ap_func
from fooof.sim.params import collect_sim_params
from fooof.sim.transform import rotate_spectrum, compute_rotation_offset
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[docs]def gen_freqs(freq_range, freq_res):
"""Generate a frequency vector.
Parameters
----------
freq_range : list of [float, float]
Frequency range to create frequencies across, as [f_low, f_high], inclusive.
freq_res : float
Frequency resolution of desired frequency vector.
Returns
-------
freqs : 1d array
Frequency values, in linear spacing.
Examples
--------
Generate a vector of frequency values from 1 to 50:
>>> freqs = gen_freqs([1, 50], freq_res=0.5)
"""
# The end value has something added to it, to make sure the last value is included
# It adds a fraction to not accidentally include points beyond range
# due to rounding / or uneven division of the freq_res into range to simulate
freqs = np.arange(freq_range[0], freq_range[1] + (0.5 * freq_res), freq_res)
return freqs
[docs]def gen_power_spectrum(freq_range, aperiodic_params, periodic_params, nlv=0.005,
freq_res=0.5, f_rotation=None, return_params=False):
"""Generate a simulated power spectrum.
Parameters
----------
freq_range : list of [float, float]
Frequency range to simulate power spectrum across, as [f_low, f_high], inclusive.
aperiodic_params : list of float
Parameters to create the aperiodic component of a power spectrum.
Length should be 2 or 3 (see note).
periodic_params : list of float or list of list of float
Parameters to create the periodic component of a power spectrum.
Total length of n_peaks * 3 (see note).
nlv : float, optional, default: 0.005
Noise level to add to generated power spectrum.
freq_res : float, optional, default: 0.5
Frequency resolution for the simulated power spectrum.
f_rotation : float, optional
Frequency value, in Hz, to rotate around.
Should only be set if spectrum is to be rotated.
return_params : bool, optional, default: False
Whether to return the parameters for the simulated spectrum.
Returns
-------
freqs : 1d array
Frequency values, in linear spacing.
powers : 1d array
Power values, in linear spacing.
sim_params : SimParams
Definition of parameters used to create the spectrum.
Only returned if `return_params` is True.
Notes
-----
Aperiodic Parameters:
- The function for the aperiodic process to use is inferred from the provided parameters.
- If length of 2, the 'fixed' aperiodic mode is used, if length of 3, 'knee' is used.
Periodic Parameters:
- The periodic component is comprised of a set of 'peaks', each of which is described as:
* Mean (Center Frequency), height (Power), and standard deviation (Bandwidth).
* Make sure any center frequencies you request are within the simulated frequency range.
- The total number of parameters that need to be specified is number of peaks * 3
* These can be specified in as all together in a flat list (ex: [10, 1, 1, 20, 0.5, 1])
* They can also be grouped into a list of lists (ex: [[10, 1, 1], [20, 0.5, 1]])
Rotating Power Spectra:
- You can optionally specify a rotation frequency, such that power spectra will be
simulated and rotated around that point to the specified aperiodic exponent.
* This can be used so that any power spectra simulated with the same 'f_rotation'
will relate to each other by having the specified rotation point.
- Note that rotating power spectra changes the offset.
* If you specify an offset value to simulate as well as 'f_rotation', the returned
spectrum will NOT have the requested offset. It instead will have the offset
value required to create the requested aperiodic exponent with the requested
rotation point.
* If you return SimParams, the recorded offset will be the calculated offset
of the data post rotation, and not the entered value.
- You cannot rotate power spectra simulated with a knee.
* The procedure we use to rotate does not support spectra with a knee, and so
setting 'f_rotation' with a knee will lead to an error.
Examples
--------
Generate a power spectrum with a single peak, at 10 Hz:
>>> freqs, powers = gen_power_spectrum([1, 50], [0, 2], [10, 0.5, 1])
Generate a power spectrum with alpha and beta peaks:
>>> freqs, powers = gen_power_spectrum([1, 50], [0, 2], [[10, 0.5, 1], [20, 0.5, 1]])
Generate a power spectrum, that was rotated around a particular frequency point:
>>> freqs, powers = gen_power_spectrum([1, 50], [None, 2], [10, 0.5, 1], f_rotation=15)
"""
freqs = gen_freqs(freq_range, freq_res)
if f_rotation:
powers = gen_rotated_power_vals(freqs, aperiodic_params,
check_flat(periodic_params), nlv, f_rotation)
# The rotation changes the offset, so recalculate it's value & update params
new_offset = compute_rotation_offset(aperiodic_params[1], f_rotation)
aperiodic_params = [new_offset, aperiodic_params[1]]
else:
powers = gen_power_vals(freqs, aperiodic_params, check_flat(periodic_params), nlv)
if return_params:
sim_params = collect_sim_params(aperiodic_params, periodic_params, nlv)
return freqs, powers, sim_params
else:
return freqs, powers
[docs]def gen_group_power_spectra(n_spectra, freq_range, aperiodic_params, periodic_params, nlvs=0.005,
freq_res=0.5, f_rotation=None, return_params=False):
"""Generate a group of simulated power spectra.
Parameters
----------
n_spectra : int
The number of power spectra to generate.
freq_range : list of [float, float]
Frequency range to simulate power spectra across, as [f_low, f_high], inclusive.
aperiodic_params : list of float or generator
Parameters for the aperiodic component of the power spectra.
periodic_params : list of float or generator
Parameters for the periodic component of the power spectra.
Length of n_peaks * 3.
nlvs : float or list of float or generator, optional, default: 0.005
Noise level to add to generated power spectrum.
freq_res : float, optional, default: 0.5
Frequency resolution for the simulated power spectra.
f_rotation : float, optional
Frequency value, in Hz, to rotate around.
Should only be set if spectra are to be rotated.
return_params : bool, optional, default: False
Whether to return the parameters for the simulated spectra.
Returns
-------
freqs : 1d array
Frequency values, in linear spacing.
powers : 2d array
Matrix of power values, in linear spacing, as [n_power_spectra, n_freqs].
sim_params : list of SimParams
Definitions of parameters used for each spectrum. Has length of n_spectra.
Only returned if `return_params` is True.
Notes
-----
Parameters options can be:
- A single set of parameters.
If so, these same parameters are used for all spectra.
- A list of parameters whose length is n_spectra.
If so, each successive parameter set is such for each successive spectrum.
- A generator object that returns parameters for a power spectrum.
If so, each spectrum has parameters sampled from the generator.
Aperiodic Parameters:
- The function for the aperiodic process to use is inferred from the provided parameters.
- If length of 2, the 'fixed' aperiodic mode is used, if length of 3, 'knee' is used.
Periodic Parameters:
- The periodic component is comprised of a set of 'peaks', each of which is described as:
* Mean (Center Frequency), height (Power), and standard deviation (Bandwidth).
* Make sure any center frequencies you request are within the simulated frequency range.
Rotating Power Spectra:
- You can optionally specify a rotation frequency, such that power spectra will be
simulated and rotated around that point to the specified aperiodic exponent.
* This can be used so that any power spectra simulated with the same 'f_rotation'
will relate to each other by having the specified rotation point.
- Note that rotating power spectra changes the offset.
* If you specify an offset value to simulate as well as 'f_rotation', the returned
spectrum will NOT have the requested offset. It instead will have the offset
value required to create the requested aperiodic exponent with the requested
rotation point.
* If you return SimParams, the recorded offset will be the calculated offset
of the data post rotation, and not the entered value.
- You cannot rotate power spectra simulated with a knee.
* The procedure we use to rotate does not support spectra with a knee, and so
setting 'f_rotation' with a knee will lead to an error.
Examples
--------
Generate 2 power spectra using the same parameters:
>>> freqs, powers = gen_group_power_spectra(2, [1, 50], [0, 2], [10, 0.5, 1])
Generate 10 power spectra, randomly sampling possible parameters:
>>> from fooof.sim.params import param_sampler
>>> ap_opts = param_sampler([[0, 1.0], [0, 1.5], [0, 2]])
>>> pe_opts = param_sampler([[], [10, 0.5, 1], [10, 0.5, 1, 20, 0.25, 1]])
>>> freqs, powers = gen_group_power_spectra(10, [1, 50], ap_opts, pe_opts)
Generate 5 power spectra, rotated around 20 Hz:
>>> ap_params = [[None, 1], [None, 1.25], [None, 1.5], [None, 1.75], [None, 2]]
>>> pe_params = [10, 0.5, 1]
>>> freqs, powers = gen_group_power_spectra(5, [1, 50], ap_params, pe_params, f_rotation=20)
Generate power spectra stepping across exponent values, and return parameter values:
>>> from fooof.sim.params import Stepper, param_iter
>>> ap_params = param_iter([0, Stepper(1, 2, 0.25)])
>>> pe_params = [10, 0.5, 1]
>>> freqs, powers, sps = gen_group_power_spectra(5, [1, 50], ap_params, pe_params,
... return_params=True)
"""
# Initialize things
freqs = gen_freqs(freq_range, freq_res)
powers = np.zeros([n_spectra, len(freqs)])
sim_params = [None] * n_spectra
# Check if inputs are generators, if not, make them into repeat generators
ap_params = check_iter(aperiodic_params, n_spectra)
pe_params = check_iter(periodic_params, n_spectra)
nlvs = check_iter(nlvs, n_spectra)
f_rots = check_iter(f_rotation, n_spectra)
# Simulate power spectra
for ind, ap, pe, nlv, f_rot in zip(range(n_spectra), ap_params, pe_params, nlvs, f_rots):
if f_rotation:
powers[ind, :] = gen_rotated_power_vals(freqs, ap, check_flat(pe), nlv, f_rot)
aperiodic_params = [compute_rotation_offset(ap[1], f_rot), ap[1]]
else:
powers[ind, :] = gen_power_vals(freqs, ap, check_flat(pe), nlv)
sim_params[ind] = collect_sim_params(ap, pe, nlv)
if return_params:
return freqs, powers, sim_params
else:
return freqs, powers
def gen_aperiodic(freqs, aperiodic_params, aperiodic_mode=None):
"""Generate aperiodic values.
Parameters
----------
freqs : 1d array
Frequency vector to create aperiodic component for.
aperiodic_params : list of float
Parameters that define the aperiodic component.
aperiodic_mode : {'fixed', 'knee'}, optional
Which kind of aperiodic component to generate.
If not provided, is inferred from the parameters.
Returns
-------
ap_vals : 1d array
Aperiodic values, in log10 spacing.
"""
if not aperiodic_mode:
aperiodic_mode = infer_ap_func(aperiodic_params)
ap_func = get_ap_func(aperiodic_mode)
ap_vals = ap_func(freqs, *aperiodic_params)
return ap_vals
def gen_periodic(freqs, periodic_params, periodic_mode='gaussian'):
"""Generate periodic values.
Parameters
----------
freqs : 1d array
Frequency vector to create peak values for.
periodic_params : list of float
Parameters to create the periodic component.
periodic_mode : {'gaussian'}, optional
Which kind of periodic component to generate.
Returns
-------
peak_vals : 1d array
Peak values, in log10 spacing.
"""
pe_func = get_pe_func(periodic_mode)
pe_vals = pe_func(freqs, *periodic_params)
return pe_vals
def gen_noise(freqs, nlv):
"""Generate noise values for a simulated power spectrum.
Parameters
----------
freqs : 1d array
Frequency vector to create noise values for.
nlv : float
Noise level to generate.
Returns
-------
noise_vals : 1d vector
Noise values.
Notes
-----
This approach generates noise as randomly distributed white noise.
The 'level' of noise is controlled as the scale of the normal distribution.
"""
noise_vals = np.random.normal(0, nlv, len(freqs))
return noise_vals
def gen_power_vals(freqs, aperiodic_params, periodic_params, nlv):
"""Generate power values for a simulated power spectrum.
Parameters
----------
freqs : 1d array
Frequency vector to create power values for.
aperiodic_params : list of float
Parameters to create the aperiodic component of the power spectrum.
periodic_params : list of float
Parameters to create the periodic component of the power spectrum.
nlv : float
Noise level to add to generated power spectrum.
Returns
-------
powers : 1d vector
Power values, in linear spacing.
Notes
-----
This function should be used when simulating power spectra, as it:
- Takes in input parameter definitions as lists, as used for simulating power spectra.
- Returns the power spectrum in linear spacing, as is used for simulating power spectra.
"""
ap_vals = gen_aperiodic(freqs, aperiodic_params)
pe_vals = gen_periodic(freqs, periodic_params)
noise = gen_noise(freqs, nlv)
powers = np.power(10, ap_vals + pe_vals + noise)
return powers
def gen_rotated_power_vals(freqs, aperiodic_params, periodic_params, nlv, f_rotation):
"""Generate power values for a simulated power spectrum, rotated around a given frequency.
Parameters
----------
freqs : 1d array
Frequency vector to create power values for.
aperiodic_params : list of float
Parameters to create the aperiodic component of the power spectrum.
periodic_params : list of float
Parameters to create the periodic component of the power spectrum.
nlv : float
Noise level to add to generated power spectrum.
f_rotation : float
Frequency value, in Hz, about which rotation is applied, at which power is unchanged.
Returns
-------
powers : 1d vector
Power values, in linear spacing.
Raises
------
ValueError
If a rotation is requested on a power spectrum with a knee, as this is not supported.
"""
if len(aperiodic_params) == 3:
raise ValueError('Cannot rotate power spectra generated with a knee.')
powers = gen_power_vals(freqs, [0, 0], periodic_params, nlv)
powers = rotate_spectrum(freqs, powers, aperiodic_params[1], f_rotation)
return powers
def gen_model(freqs, aperiodic_params, periodic_params, return_components=False):
"""Generate a power spectrum model for a given parameter definition.
Parameters
----------
freqs : 1d array
Frequency vector to create the model for.
aperiodic_params : 1d array
Parameters to create the aperiodic component of the modeled power spectrum.
periodic_params : 2d array
Parameters to create the periodic component of the modeled power spectrum.
return_components : bool, optional, default: False
Whether to also return the components of the model.
Returns
-------
full_model : 1d array
The full power spectrum model, in log10 spacing.
pe_fit : 1d array
The periodic component of the model, containing the peaks.
Only returned if `return_components` is True.
ap_fit : 1d array
The aperiodic component of the model.
Only returned if `return_components` is True.
Notes
-----
This function should be used when computing model reconstructions, as it:
- Takes in input parameter definitions as arrays, as used in FOOOF objects.
- Returns the power spectrum in log10 spacing, as is used in FOOOF models.
"""
ap_fit = gen_aperiodic(freqs, aperiodic_params)
pe_fit = gen_periodic(freqs, np.ndarray.flatten(periodic_params))
full_model = pe_fit + ap_fit
if return_components:
return full_model, pe_fit, ap_fit
else:
return full_model